Valen had 140 more marbles than Peter. Valen gave 20% of his marbles to Peter. Peter in return gave 50% of his marbles to Valen. In the end, Valen had 508 more marbles than Peter. How many marbles did Valen have at first?
| |
Valen |
Peter |
Comparing Valen
and Peter at first |
140 more |
|
| Before |
5 u + 140 |
5 u |
| Change 1 |
- 1 u - 28 |
+ 1 u + 28 |
| After 1 |
4 u + 112 |
6 u + 28 |
| Change 2 |
+ 3 u + 14 |
- 3 u - 14 |
| After 2 |
7 u + 126 |
3 u + 14 |
20% =
20100 =
1520% x 140
=
20100 x 140
= 28
50% x 28
=
50100 x 28
= 14
50% x 6 u
=
50100 x 6 u
= 3 u
Valen had 508 more marbles than Peter in the end. If another 508 marbles are given to Peter, both will have the same number of marbles.
7 u + 126 = 3 u + 14 + 508
7 u - 3 u = 14 + 508 - 126
11 u = 396
1 u = 396 ÷ 11 = 36
Number of Valen's marbles at first
= 5 u + 140
= 5 x 36 + 140
= 180 + 140
= 320
Answer: 320
